Regardless of the specific make and model: all devices of this type contain an optical disc drive that has two major sub-components:

a motor with a spindle assembly to hold and rotate the disc

a laser assembly that moves radially and reads the disc (from the center outwards)

If the player is having trouble loading or reading discs, the problem is almost always mechanical. Try these quick tricks:

nudge / slide the laser assembly back and forth in its track, using your finger or some sort of plastic tool like a spudger or a pen cap

clean the laser lens (with 90% isopropyl alcohol and a q-tip)

The vast majority of optical disc drives will spring back to life after step 1 and/or step 2 above. If neither of those works, confirm that there isn't foreign matter like hair wrapped around the motor spindle or a dust bunny in the CD tray slot or mechanism.

If the laser assembly is moving well, the motor is spinning freely and you're sure there's no foreign matter in the drive then it is possible the laser has stopped working.

Try removing and reseating the ribbon cable to the laser assembly. If that doesn't work then the laser might have burnt out. (Depending on the design of the optical drive you might be able to use a transparent disc (you get one or two of these when you buy a stack of discs) to see if the laser is indeed lasing.) A burnt-out laser is a hard repair because you have to identify and replace the part.

If you try nudging the laser a few times unsuccessfully as mentioned above, notice where you left it last time and see if it moves in its track at all when you try the next time. If not, it's possible that the ribbon cable to the laser assembly came loose or needs to be reseated. (You should also hear noise as the laser assembly moves back and forth trying to find the beginning of the disc.)

Confirm that the (tiny!) plastic lens is indeed still on the laser assembly: we've seen one optical drive where the lens popped loose and was rattling around in the case: gluing it back fixed the optical drive.

If you open the case: It's always worth it to visually inspect any capacitors to see if they're bulging at the top: they could keep the laser from working even if everything else seems to be OK.

Tray door hint: Console-style players usually have a plastic cosmetic trim piece on the front of the tray door slot that needs to be removed to get full access to the drive. it usually comes off by pushing it up, but it _might_ be secured with screws.

Disc problems: If the problem is reading a specific disc e.g. freezing or stuttering (like with heavily used discs borrowed from the library): lightly polish any scratches on the disc with an abrasive toothpaste (like Colgate or Crest) or with a paste car wax: emphasize radial strokes in your buffing, i.e. going from the center to the edge and vice-versa. If a specific disk won't read at all: look for heavy scratches towards the center and emphasize polishing those (optical discs read from the center out, and the laser can't find track 0 to start reading the disc.)